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Puzzle - Rate

At midnight at the start of Monday, January 1st, Professor Stone set two of his old fashioned clocks to the correct time.

One of his clocks gains one minute every hour and the other loses two minutes every hour.

1. When will the clocks next show the same time as each other?
2. When will the clocks both show the correct time?

[Ref: ZDJB] © Kevin Stone

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